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Let Y 1 and Y 2 be independent standard normally distributed random variables. Find the
distribution of the random variable U = Y 1 Y 2 (a) Write an expression for the cdf of U . (b)
Find the probability density function of U . (c) Find the conditional distribution of U , given Y 1 .

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  • 1. Let Y 1 and Y 2 be independent standard normally distributed random variables. Find the distribution of the random variable U = Y 1 Y 2 (a) Write an expression for the cdf of U . (b) Find the probability density function of U . (c) Find the conditional distribution of U , given Y 1 .